We should take in the children, process them, feed them, and give them the care they deserve as humans. If they have relatives in the country, I'd support giving them limited amnesty from a humanitarian point of view. Those without relatives in the country should be deported in a timely manner.
That's pretty much my take on it as well. Not an ideal solution, of course. I'd also consider finding ways to make those relatives legit, when possible. The only really weird cases are those who don't have people we can find here. How do we deport them safely? And into what life are we deporting them? Do we have the means to import their parents?
Ah, where's CARLHAYDEN when you need him?